This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A140315 #25 Jul 18 2025 04:52:11
%S A140315 4,5,8,34,280,281
%N A140315 Numbers k such that k!/k#-1 and k!/k#+1 are a twin prime pair.
%C A140315 4,5 and 280,281 result in the same respective twin prime pairs. Using gmp, testing n < 4000, the last 3-prp found was the 8897 digit 3-prp, 3337!/3337#-1.
%H A140315 G. L. Honaker, Jr. and Chris Caldwell, <a href="https://t5k.org/curios/cpage/2777.html">Prime Curios! 281</a>.
%F A140315 n# is the primorial function A034386(n).
%F A140315 A140293 INTERSECT A140294. - _R. J. Mathar_, Feb 27 2012
%e A140315 8!/8#-1 = 191, 8!/8#-1 = 193. 191 and 193 form a twin prime pair.
%t A140315 Primorial[n_] := Product[Prime[i], {i, 1, PrimePi[n]}];
%t A140315 Select[Range[
%t A140315 1000], (p = (#! / Primorial[#]);
%t A140315 PrimeQ[p + 1] && PrimeQ[p - 1]) &] (* _Robert Price_, Oct 11 2019 *)
%o A140315 (PARI) g(n) = for(x=1,n,y=x!/primorial(x)-1;z=nextprime(y+1); if(ispseudoprime(y)&&z-y==2,print1(x", ")))
%o A140315 primorial(n) = { local(p1,x); if(n==0||n==1,return(1)); p1=1; forprime(x=2,n,p1*=x); return(p1) }
%Y A140315 Cf. A001097, A034386, A049614, A140293, A140294.
%K A140315 nonn,hard,more
%O A140315 1,1
%A A140315 _Cino Hilliard_, May 25 2008
%E A140315 Offset corrected by _Amiram Eldar_, Jul 18 2025